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On the Davenport constant and on the structure of extremal zero-sum free sequences

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Abstract

Let \(G = C_{n_1 } \oplus \cdots \oplus C_{n_r }\) with 1 < n 1 | … | n r be a finite abelian group, d*(G) = n 1 +…+n r −r, and let d(G) denote the maximal length of a zerosum free sequence over G. Then d(G) ≥ d*(G), and the standing conjecture is that equality holds for G = C r n . We show that equality does not hold for C 2 ⊕ C r2n , where n ≥ 3 is odd and r ≥ 4. This gives new information on the structure of extremal zero-sum free sequences over C r2n .

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Authors and Affiliations

  1. Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, Heinrichstraße 36, 8010, Graz, Austria

    Alfred Geroldinger, Manfred Liebmann & Andreas Philipp

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  1. Alfred Geroldinger
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  2. Manfred Liebmann
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  3. Andreas Philipp
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Correspondence to Alfred Geroldinger.

Additional information

Communicated by Attila Pethő

This work was supported by the Austrian Science Fund FWF, Project No. P21576-N18. We kindly acknowledge the support of the DECI (Distributed Extreme Computing Initiative) within the muHEART project for providing access to the cineca supercomputer.

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Geroldinger, A., Liebmann, M. & Philipp, A. On the Davenport constant and on the structure of extremal zero-sum free sequences. Period Math Hung 64, 213–225 (2012). https://doi.org/10.1007/s10998-012-3378-6

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  • DOI: https://doi.org/10.1007/s10998-012-3378-6

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